Abstract:This
paper presents a dynamic model of a rotating beam with a tip mass undergoing
large angle, high speed maneuvering. This type of model may also be useful in
modeling, analysis and development of various inertial sensors and transducers
with similar operating principles. With the consideration of the second-order
term of the coupling deformation field, the complete first-order approximated
model (CFOAM) of a flexible spacecraft system is developed by using assumed mode
method (AMM) and Lagrangian principle. A first-order approximated model (FOAM)
is obtained by neglecting the high order terms of the generalized coordinates in
CFOAM. A lower order simplified first-order approximated model (SFOAM) is
derived by deleting the terms related to the axial deformation. Numerical
simulations and theoretical analysis show that: (i) the second-order term has a
significant effect on the dynamic characteristics of the system and the dynamic
stiffening is accounted for, while the traditional linear approximated model (TLAM)
presents invalid simulation results; (ii) the end mass has a ‘stiffening’ effect
on the flexible system in FOAM, but a ‘softening’ effect in TLAM; and (iii) the
SFOAM describes the dynamic behavior well and can be used for controller design.